Nonparametric estimation of conditional probability distributions using a generative approach based on conditional push-forward neural networks
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| Format: | Preprint |
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2025
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| author | Franco, Nicola Rares Tedesco, Lorenzo |
| author_facet | Franco, Nicola Rares Tedesco, Lorenzo |
| contents | We introduce conditional push-forward neural networks (CPFN), a generative framework for conditional distribution estimation. Instead of directly modeling the conditional density $f_{Y|X}$, CPFN learns a stochastic map $φ=φ(x,u)$ such that $φ(x,U)$ and $Y|X=x$ follow approximately the same law, with $U$ a suitable random vector of pre-defined latent variables. This enables efficient conditional sampling and straightforward estimation of conditional statistics through Monte Carlo methods. The model is trained via an objective function derived from a Kullback-Leibler formulation, without requiring invertibility or adversarial training. We establish a near-asymptotic consistency result and demonstrate experimentally that CPFN can achieve performance competitive with, or even superior to, state-of-the-art methods, including kernel estimators, tree-based algorithms, and popular deep learning techniques, all while remaining lightweight and easy to train. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2511_14455 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Nonparametric estimation of conditional probability distributions using a generative approach based on conditional push-forward neural networks Franco, Nicola Rares Tedesco, Lorenzo Machine Learning Methodology We introduce conditional push-forward neural networks (CPFN), a generative framework for conditional distribution estimation. Instead of directly modeling the conditional density $f_{Y|X}$, CPFN learns a stochastic map $φ=φ(x,u)$ such that $φ(x,U)$ and $Y|X=x$ follow approximately the same law, with $U$ a suitable random vector of pre-defined latent variables. This enables efficient conditional sampling and straightforward estimation of conditional statistics through Monte Carlo methods. The model is trained via an objective function derived from a Kullback-Leibler formulation, without requiring invertibility or adversarial training. We establish a near-asymptotic consistency result and demonstrate experimentally that CPFN can achieve performance competitive with, or even superior to, state-of-the-art methods, including kernel estimators, tree-based algorithms, and popular deep learning techniques, all while remaining lightweight and easy to train. |
| title | Nonparametric estimation of conditional probability distributions using a generative approach based on conditional push-forward neural networks |
| topic | Machine Learning Methodology |
| url | https://arxiv.org/abs/2511.14455 |